簡約 4^{-2((ln(3))/(2ln(2)))}

解

簡約

4^{- 2 (\frac{l n ( 3 )}{2 l n ( 2 )})}

\frac{1}{4 ^{\frac{l n ( 3 )}{l n ( 2 )}}}

十進法表記

0.11111 \dots

解答ステップ

4^{- 2 (\frac{l n ( 3 )}{2 l n ( 2 )})}

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{4 ^{2 \cdot \frac{l n ( 3 )}{2 l n ( 2 )}}}

4^{2 \cdot \frac{l n ( 3 )}{2 l n ( 2 )}} = 4^{\frac{l n ( 3 )}{l n ( 2 )}}

= \frac{1}{4 ^{\frac{l n ( 3 )}{l n ( 2 )}}}